HONG KONG, Nov 2 (Reuters) - South Korea's biggest low-cost carrier, Jeju Air, is in talks with Airbus and Boeing to buy 50 narrowbody jets as it expands a network that includes one of the world's busiest routes, sources close to the matter said.

The potential purchase, worth around $5.7 billion at list prices, offers Europe's Airbus a chance to trigger the defection of a Boeing customer in a key market but Boeing is seen as the front-runner to win the order and retain the 737 operator's business, the sources said.

Airbus and Boeing declined to comment. An official with Jeju Air said the company was reviewing prices for aircraft.

Those include what in 2017 represented the world's busiest single route, linking the capital Seoul to the popular resort island of Jeju, according to air travel data firm OAG.

South Korea’s six no-frills carriers saw the number of passengers using international routes quadruple to 20.3 million in 2017 from 4.9 million in 2013, according to South Korea’s transport ministry.

Airbus and Boeing are competing fiercely for new orders as an extended airliner industry boom shows signs of faltering. Both planemakers are sold out for several years.

"Jeju Air cannot confirm such a statement on the company's potential plane order, but we have requested both Airbus and Boeing for estimates for plane purchases to internally review prices," an official from Jeju Air told Reuters. (Reporting by Anshuman Daga, Heekyong Yang, Tim Hepher; Editing by Muralikumar Anantharaman)